In triangle ABC, ∠A = 30°, ∠B = 105° and the side a = 8 cm. The length of side c is:

First C = 180° − 30° − 105° = 45°. The sine rule then gives c = a·sinC/sinA = 8 × (√2/2)/(1/2) = 8√2 ≈ 11.31 cm. Turning the ratio upside down gives a·sinA/sinC = 4√2 ≈ 5.66 cm, which is shorter than a even though c faces the larger angle — an immediate warning sign. The common ratio a/sinA = 16 is the circumdiameter, not a side, and 8√3 would follow from mistakenly taking C = 60°.